数#

Real Numbers(ℝ):实数 Integers(Whole Numbers)(ℤ):整数 Natural numbers(ℕ):自然数(不包括0？查一下syllabus) 正整数(N+)(N*) Rational Numbers(Q):有理数 A factor: 因数 A multiple:倍数 index/order/exponents:指数 reciprocal:倒数

quotient:商 Approximately equal to:约等于 identical to:全等于 bracket:括号 竖式 乘法 除法

集合#

{(x, y) : y = 2x + 1}

E set

∅ set

n(∅) = 0

upper case: set , lower case: element

a ∈ A means a is an element of A

A ⊆ B means A is a subset of B

A ⊂ B means A is a proper subset of B (A≠B)

A∩B intersection A∪B union A’ not A

质因数 (与最大公因数最小公倍数)#

Prime tree prime factor decomposition (PFD) indices are even: square number indices are multiples of 3: cube number the highest common factor (HCF)最大公因数 the lowest common multiple (LCM)最小公倍数

指数运算&科学表达式#

base number: 底数 index: 指数

square root:平方根 cube root:立方根 A nth root standard form: 科学表达式

分数#

numerator: 分子 denominator: 分母 mixed numbers: 带分数 improper fraction(top heavy fraction): 假分数

比例#

A multiplier, p, is the decimal equivalent of a percentage increase or decrease

利息#

simple interest: 单利 compound interest: 复利 depreciation: 约等于复利 substitute: 代入 decay: 下降

FDP#

terminating decimal: 有限小数 recurring decimal: 无限循环小数 错位相减

Ratio#

direct proportion: 正比 inverse proportion: 反比

Compound Measures#

没啥好说的

时间 货币 转换#

millennium: 千年 midday: 12pm midnight: 12am am/pm : 12 1 2 3 4 5 6 7 8 9 10 11

Each column represents a different bus/train – these are often called “services”

The time in each cell usually indicate departure times(when the bus/train leaves that stop/station)

The last location on the list usually shows the arrival time

GBP: 英镑£

汇率类问题单独开一行写A货币比B货币等于几比几，下面一行写x:几几几。再用除法算出scale factor

钱要保留两位小数！！！！

近似 估计 边界#

estimate: 一般一个sf

LB <= x < UB

计算：x+-一半精度

计算器#

负数：(-) rounding 不必在计算中进行，用3.1415…省略号表示

基础#

term: 单项式 coefficient: 系数 constants: 常数 expression: 表达式 equation: 方程/等式 formula: 公式(F=ma) inequality: 不等式 substitution: 代入 v=u+at v2-u2=2as s=ut+0.5at2 “like” terms: 同类项

a^x=a^y x=y

指数根号#

展开括号，因式分解#

expanding: 展开 factorisation: 因式分解 quadratic expression: 二次表达式 monic quadratic expression: a=1 non-monic : a!=1 十字相乘 discriminant: 判别式(b2-4ac)

线性方程，不等式#

二次方程#

completing the square: a(x+p)2+q quadratic formula: 二次方程求根公式 repeated root: 两个相同的根

重整式子#

(rearrange formulae) (changing the subject)

联立方程#

linear simultaneous equations: 线性方程组 Elimination: 加减消元 substitution: 代入

分式#

分式: Algebraic Fractions

列方程解方程#

5 lots of something: 5x polygon: 多边形 parallelogram: 平行四边形 rhombus: 菱形 prisms: 柱体 pyramids: 锥体 regular polygon: 正多边形 interpret: 解释

函数#

Composite(compound) functions: 复合函数 Inverse Functions: 反函数

数列#

Sequences: 数列 term: 项 position: 索引(ish?) position-to-term rule: 通项公式 term-to-term rule: 由an前面的项得到an linear(arithmetic)/quadratic(二次序列)/geometric(等比序列) sequences cubic sequence: the third differences are constant common ratio: 公比 common difference: 公差

a fibonacci sequence: 泛指an=a(n-1)+a(n-2)的序列，可以改变前两项 the fibonacci sequence: 前两项为1

求quadratic sequence的a: the second difference 除以二 剩下的用原数列减an2,得到一个等差数列

坐标系#

steep: 陡峭的 求斜率：rise over run Pythagoras’ Theorem: 勾股定理

线型图象#

ax+by+c=0 -> 斜率: -a/b 截距: -c/b parallel: 平行(相同的直线不是平行) the negative reciprocal: 倒数取反

二次图像#

parabola: 抛物线

更多图像和切线#

解不等式#

有等号的用实线，否则用虚线 要shade unwanted的area

生活中的图像#

conversion/convert: 转换 deceleration: 减速

微分#

the derivative: 导数 the derived function: 导函数 f’(x) -> f-dashed-of-x Turning points/stationary points: 导数为0的点 peak/trough: 峰/谷 positive cubic: 左边最大值，右边最小值 negative cubic: 左边最小值，右边最大值 d2y/dx2 optimisation/optimal: 优化

基本#

symmetry: 对称 the order of rotational symmetry: 转一圈有几次和自己一样 (有的时候order是1也会说成没有rotational symmetry) n lines of symmetry(有n条对称轴) mirror line polygon: 多边形 cuboid: 长方体 cylinder: 圆柱

1. triangle
2. quadrilateral
3. pentagon
4. hexagon
5. heptagon
6. octagon
7. nonagon
8. decagon

cube: 9 planes of symmetry 一般来说，柱体的planes of symmetry是横截面的对称轴数量加1 而锥体的是横截面对称轴数量 equilateral triangle: 等边三角形 isosceles triangle: 等腰三角形 parallelograms: 平行四边形 rhombuses(rhombi): 菱形 trapezium: 梯形（一对边平行） kite: 两组邻边相等的四边形 bisect: 平分 obtuse angle: 钝角 acute angle: 锐角 dagonal: 对角线 perimeter: 周长 circumference: 圆的周长

prism: 柱体 pyramid: 锥体 square-based pyramid cone: circular base tetrahedron: base is an equilateral triangle

face/vertex(vertices)/edge

net: 展开图

1cl = 10 ml

1 hectare (ha) = 10 000 m2

多边形和平行线里的角#

basic angle properties:

1. Angles that meet at a point add up to 360°
2. Angles that meet at a point on a straight line add up to 180°
3. Vertically opposite angles are equal(对顶角相等) regular polygon: 正多边形

sum of interior angles = 180° × (n-2) 外角(exterior angle)和永远为360°

Corresponding angles are equal(同位角相等) Alternate angles are equal(内错角相等) Allied (co-interior) angles add to 180°(同旁内角互补) (on parallel lines)

transverse: 跨过两个平行线的直线

bearings constructions & scale drawings#

bearing: 从北方开始顺时针测量，保留三位有效数字，不写degree symbol (画图记得画north line) 面积用A(Area)

圆#

所有的circle theorem在考试中都要写出来 Circle Theorem: The angle subtended by an arc at the centre is twice the angle at the circumference(这个定理必须写出来) Circle Theorem: The angle in a semicircle is a right angle(俺也一样)

chord(弦) Any equal chords are equidistant from the centre of the circle Circle Theorem: The perpendicular bisector of a chord is a radius Circle Theorem: A radius and a tangent meet at right angles Two tangents from a circle to the same point outside of a circle are equal

cyclic quadrilaterals(圆内接四边形) Circle theorem: Opposite angles in a cyclic quadrilateral add up to 180°

Circle Theorem: Angles at the circumference subtended by the same arc are equal(Angles in the same segment are equal) Circle Theorem: Alternate Segment Theorem(弦切角定理)

面积和周长#

compound shapes: 由多个简单图形拼接出来的图形 rectangle: A=lw triangle: A=1/2 bh trapezium: A=1/2 (a+b)h parallelogram: A=bh

圆和扇形和弧#

arc:弧 minor arc(劣弧) major arc(优弧) sector: 扇形 minor sector major sector

体积和表面积#

volume: 体积 volume of a pyramid: 三分之一底乘高 圆的体积：4/3 πr3 frustum: 圆台

surface area: 表面积 slant height: 斜高 surface area of a sphere = 4πr2

全等和相似(congruence & similarity)#

congruent/congruence: 全等 SAS,ASA,AAS,SSS,RHS similar: 相似 证明任意多边形相似：对应边成比例 三角形：AAA Equivalent: 对应的

直角三角形#

Pythagoras’ Theorem: 勾股定理 hypotenuse: 斜边 opposite: 对边 Adjacent: 邻边

Trigonometry: 三角学 sin: 奇函数 cos: 偶函数

the angles of elevation and depression

sine, cosine rule & 三角形面积#

the sine rule: a/sinA = b/sinB = c/sinC the cosine rule: cosA = (b2+c2-a2) / 2bc or a2=b2+c2 - 2bc cosA

A = 1/2 ab sinC 表示角的方法: ABC上面加一个^

三维三角函数#

d2=a2+b2+c2

三角函数图像和方程#

先label出关键点，再连接成线

向量#

magnitude direction translation vector scalar: 标量 magnitude(modulus): |a| specific vector: AB-> general vector: a 证明三点共线：找出两个向量平行

变化#

original shape: object(A,B,C) transformed shape: image(A’,B’,C’)

translation Shape A has been translated using the vector (一个向量)

reflection

Shape A has been reflected in the line x=-1 to create shape B

rotation Rotation, 90o clockwise with centre (-4, 0) enlargement The length scale factor is 2, therefore the area scale factor will be 2^2 = 4, hence, the area of C’ is 4 times larger than C

Shape A has been enlarged using a scale factor of 3 and a centre of enlargement (9, 9) to create shape B

C.o.E

objection

基础#

An experiment is a repeatable activity that has a result that can be observed or recorded Trials are what we call the repeats of the experiment An outcome is a possible result of a trial An event is an outcome or a collection of outcomes A sample space is the set of all possible outcomes of an experiment The probability of event A is denoted as P(A)

The complement of event A is the event where event A does not happen A’ mutually exclusive events: 发生了A就不可能发生B，A交B为空集

sample space: 所有可能的结果 possibility diagram: combining two things using a grid

Relative frequency(estimate probabilities from experimental data)

expected frequency(the number of times you would expect a particular outcome to occur when repeating a trial numerous times)

概率图像#

Two Way Tables The row/column totals are sometimes called marginal (or sub-) totals Where the row totals and column totals meet, we have the grand total Conditional probabilities are sometimes written using the ‘straight bar’ notation P(A|B)

Venn Diagrams

Tree Diagrams

conditional probability#

平均和极差#

统计图像#

Histogram(直方图)#

cumulative frequency & box plots#

Correlation is a way of describing the way two quantities are related to each other

positive/negative/no coorelation

correlation doesn’t mean causation

scatter graphs & correlation#